I think if we look at the story carefully we can see that it actually is a peace offering and a final acceptance on the part of the mother that her daughter has chosen her own way and she cannot pressurise her any more to be something that she doesn't want to. Note how when Jing-Mei's mother tells her that she can pick up the piano again quickly, she says these words to Jing-Mei without emotion:

"You just not trying," said my mother. And she was neither angry or sad. She said it as if to announce a fact that could never be disproved. "Take it," she said.

The absence of emotion is a key factor that supports Jing-Mei's interpretation of this offering as a "sign of forgiveness, a tremendous burden removed." Finally, her mother has accepted her on her own terms rather than constantly wishing and forcing her to be who she wasn't. The fact that Jing-Mei regards the piano as a "shiny trophy" indicates that she sees that she has been victorious in winning the conflict against her mother.